It never was hard to figure why a certain football coach might want to make a run for the U.S. Senate, not if you try to understand the social circumstances in the state of Georgia and how the people have a big love for the fellows who win ballgames and keep the glory close to home. And not if you try to understand Vince Dooley, the former student of southern political history who also boasted the best four-year record in college football through 1983.

For the last 21 years, Dooley has run the show at the university in Athens and, in the process, earned a reputation as a man of good smarts and wit and dignity. Not only distinguished, Dooley also managed to lead his team to the national championship in 1980. An old Georgia politician once said meeting Dooley for the first time, you might think him an assistant professor of English or some such, he was that bright and polished. But a football coach?

Back in June, Dooley said he would take about 30 days to decide whether to challenge Mack Mattingly, the incumbent Republican, in 1986. The announcement came during a crowded news conference at Hartsfield International Airport in Atlanta, the very day Dooley and his wife Barbara took off on a 12-day European vacation with 35 Bulldog supporters, including Herman Talmadge, a four-term senator and Democrat who lost to Mattingly in President Reagan's first landslide.

Dooley, himself a Democrat who describes his politics as "situated somewhere between conservative to moderate," said he would resign as football coach before the season opener if he did decide to run, but hoped to remain as athletic director until he began campaigning actively in January. He said his heart told him one thing and his mind told him another. But he did not say which was saying to run and which was saying to coach.

Earlier this week, the day after Georgia lost, 20-16, to Alabama in a nationally televised game, Dooley drove his big red sedan to a campus dormitory for lunch. He walked through the service line wearing gray slacks, a bright red blazer and a pin-striped polo shirt with a bulldog stitched over the breast pocket. Somebody said, "You want one roast beef sandwich, Coach, or do you want two?" And Dooley said, "One with gravy, please."

Big as it was, nobody could ever convince him that Vince Dooley was undeserving of the dream to run for public office. He was a coach, but he was concerned, he said, that this country find good leaders. And he felt a certain call to duty, always had. He said he didn't want to pretend that it wouldn't have sounded nice having U.S. senator instead of coach tacked before his name, but it wasn't an ego thing that led him to create such a furor, and it wasn't an ego thing that led him to announce his plans not to run in late July, only five weeks before the season opener.

"Anybody with any ambition has an ego," Dooley said this week. "But there's a danger in having one. The danger is that it may be excessive. I tried to make sure that it was not a driving force with me when trying to make up my mind, that it was there because it was necessary for it to be there."

In the final analysis, Dooley said, he could not in good conscience end his longtime commitment and responsibility to the football team and the University of Georgia. What it all came down to, he said, was Vince Dooley figuring he owed somebody something, and knowing that that obligation could not be fulfilled while stumping across the red clay hills of Georgia, telling people he belonged in Washington then having to explain why he wasn't up in Athens, making sure the 'Dawgs hunkered down.

"I'm a little naive," Dooley said. "The response (to the announcement) was a little more than I ever expected. When I came back from Europe, I didn't think anybody would be at the airport. I thought maybe there'd be a couple of old friends wanting to know how the trip went. But the people . . . Everybody wanted to know, 'What's your decision.' "

Dooley had felt confident Mattingly was headed for defeat, considering the state traditionally had elected Democrats to Congress. But Mattingly apparently had gained much public support and emerged as a formidable opponent. In June, President Reagan had made an appearance at a fund-raising dinner in a suburb of Atlanta and helped pull in about $500,000 for Mattingly's campaign. Also, the university president told Dooley that he had to sever all ties with the school if he decided to seek public office. Dooley had hoped to remain as the athletic director while quietly drumming up support and the $2 million to $4 million necessary to wage a successful campaign come January.

"Again, I was naive," Dooley said. "What I was thinking, I could stay on until after the season because there was no active campaigning to do. Normal people would be able to do such a thing. But I'm not normal in that respect. The attention that I get and the demands would not have let everything settle down while I was the athletic director. There just would have been too much tension and too much controversy."

But Dooley, who celebrated his 53rd birthday Wednesday, is no stranger to controversy. This year, an NCAA investigation uncovered violations and placed Georgia's football and basketball teams on probation. Although the sanctions do not prohibit the Bulldogs from postseason play or appearances on national TV, the NCAA reduced the number of scholarships the football program could offer over the next two years. On top of that, recruiting restrictions were placed on members of the basketball staff who broke NCAA rules by giving rides and athletic equipment to recruits.

"It was an embarrassment," Dooley said. "And I'm the one who's ultimately responsible. At the same time, I'm not hanging my head down. I think we do a good job abiding by the rules. But evidently, it was not good enough."

Dooley said the investigation was "extensive and intense," and found that "there were no football staff members involvement in any kind of recruiting violation." The most serious charge against the football program involved a booster who, in 1982, helped a player obtain a loan to pay off a car.

Dooley also suffered some embarrassment when the Macon Telegraph and News, in a Pulitzer Prize-winning, 18-part series, revealed that only 17 percent of Georgia's black football players and 50 percent of its white earned degrees over the last 10 years. Dooley said it bothered him that the newspaper looked into only the Georgia athletic program and not the entire Southeastern Conference. He also said that some of the figures reported in the series were "distorted" and "misleading."

"I don't mind the standard that we've set here at Georgia," Dooley said. "And I think it's good to have critics question things, mainly because it makes you go back and examine your conscience. You ask yourself: Am I doing what is right? Am I doing the right thing? The only way you can answer those questions is by looking back at the standards you set."

As a would-be candidate for public office, Dooley did not respond to any issues or ever speak with Mattingly. He said he'd read in an Atlanta newspaper that Mattingly would remain a devoted Georgia fan whether Dooley decided to run or not, and knew "that not being a Bulldog fan could mean a lot of trouble for a politician in this state."

Dooley said he received "lots and lots of mail, most of it positive. Those that were negative were from Republicans saying: 'Coach, you've put me in a tough decision.' "

When, on July 25, Dooley announced that he would not run for the Senate in 1986, he did not rule out the possibility of one day running for a public office. He said this week, "My plans are to coach football. People ask me if I'll never consider politics. Naturally, I say no, that doesn't mean that."

In July, Barbara Dooley told a reporter for the Atlanta Journal that she wouldn't mind one day moving from Athens to the Governor's Mansion on West Paces Ferry Road in Atlanta. "I think it would be spectacular to live on West Paces Ferry Road," she said. "But you know, it isn't bad living on Milledge Court in Athens, Ga."